Erdős Problem #709
Prior state unknown→proved
upper bound improved to f(n) ≤ 14n^{3/7} with an explicit logarithmic lower bound; matching bounds remain open
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number-theory / Extremal Divisibility
Erdős Problem #709
How long must an interval be to contain distinct representatives $x_i$, with $a_i \mid x_i$, for every $n$-element set of moduli $A = \{a_1, \dots, a_n\}$?
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How long must an interval be to contain distinct representatives $x_i$, with $a_i \mid x_i$, for every $n$-element set of moduli $A = \{a_1, \dots, a_n\}$?
upper bound improved to f(n) ≤ 14n^{3/7} with an explicit logarithmic lower bound; matching bounds remain open
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